Cos90

What is the relation among all the trigonometrical ratios of (90° + θ)? In trigonometrical ratios of angles (90° + θ) we will find the relation between all six trigonometrical ratios. Let a rotating line OA rotates about O in the anti-clockwise direction, from initial position to ending position makes an angle ∠XOA = θ again the same rotating line rotates in the same direction and makes an angle ∠AOB =90°. Take a point C on OA and draw CD perpendicular to OX or OX’. Again, take a point E on OB such that OE = OC and draw EF perpendicular to OX or OX’. From the right-angled ∆ OCD and ∆ OEF we get, ∠COD = ∠OEF [since OB ⊥ OA] and OC = OE. Therefore, ∆ OCD ≅ ∆ OEF (congruent). Therefore according to the definition of trigonometric sign, OF = - DC, FE = OD and OE = OC We observe that in diagram 1 and 4 OF and DC are opposite signs and FE, OD are either both positive. Again we observe that in diagram 2 and 3 OF and DC are opposite signs and FE, OD are both negative. According to the definition of trigonometric ratio we get, sin (90° + θ) = \(\frac\) ● Trigonometric Functions • • • Reciprocal Relations of Trigonometric Ratios • • • • • • • • Trig Ratio Problems • Proving Trigonometric Ratios • • • • • • • • • • • • • • Trigonometrical Ratios of (- θ) • • • Trigonometrical Ratios of (180° + θ) • Trigonometrical Ratios of (180° - θ) • Trigonometrical Ratios of (270° + θ) • T • Trigonometrical Ratios of (360° + θ) • • • • • Trigonometric Functions of any Angles • • 11 and 12 Grade M...

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Cos 90 Degrees The value of cos 90 degrees is 0. Cos 90 degrees in radians is written as cos (90°×π/180°), i.e., cos (π/2) or cos (1.570796. . .). In this article, we will discuss the methods to find the value of cos 90 degrees with examples. • Cos 90°: 0 • Cos (-90 degrees): 0 • Cos 90° in radians: cos (π/2) or cos (1.5707963 . . .) What is the Value of Cos 90 Degrees? The value of cos 90 degrees is 0. Cos 90 degrees can also be expressed using the equivalent of the given We know, using ⇒ 90 degrees = 90°× (π/180°) rad = π/2 or 1.5707 . . . ∴ cos 90° = cos(1.5707) = 0 Explanation: For cos 90 degrees, the angle 90° lies on the positive y-axis. Thus cos 90° value = 0 Since the cosine function is a ⇒ cos 90° = cos 450° = cos 810°, and so on. Note: Since, cosine is an Methods to Find Value of Cos 90 Degrees The value of cos 90° is given as 0. We can find the value of cos 90 • Using Trigonometric Functions • Using Unit Circle Cos 90° in Terms of Trigonometric Functions Using • ±√(1-sin²(90°)) • ± 1/√(1 + tan²(90°)) • ± cot 90°/√(1 + cot²(90°)) • ±√(cosec²(90°) - 1)/cosec 90° • 1/sec 90° Note: Since 90° lies on the positive y-axis, the final value of cos 90° will be 0. We can use trigonometric identities to represent cos 90° as, • -cos(180° - 90°) = -cos 90° • -cos(180° + 90°) = -cos 270° • sin(90° + 90°) = sin 180° • sin(90° - 90°) = sin 0° Cos 90 Degrees Using Unit Circle To find the value of cos 90 degrees using the unit circle: • Rotate ‘r’ anticlockwise to form 90° angle w...

What is the Value of Cos 90 Degrees: The sine function, cosine function, and tangent function are the three most well-known trigonometric ratios in trigonometric functions. It is commonly specified for angles smaller than a right angle. Trigonometric functions are written as the ratio of two sides of a right triangle containing the angle, the values of which may be found in the length of various line segments around a unit circle. Degrees are often represented as 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360°. The first quadrant is considered to be located between 0 degreesand 90degrees. The third quadrant has angles between 180 degreesand 270 degrees, whereas the second quadrant contains angles ranging between 90 degreesand 180 degrees. The fourth quadrant covers the range of 270 degreesto 360 degrees. In the fourth quadrant, Cos stays positive. It is important to note that everything in the first one is positive. Tan is also positive in the second and third quadrant. For example, the distance from a point to the origin stays positive, but the X and Y coordinates might be either negative or positive. Thus, in the first quadrant, all coordinates are positive, but in the second quadrant, only sine and cosecant are positive. Tangent and cotangent are only positive in the third quadrant, but cosine and secant stay positive in the fourth. Let us now look at the value for cos 90 degrees, which is equal to zero, and how the values are calculated using the quadrants of a unit circl...

Note that the image below is only for #x# in Q1 (the first quadrant). If you wish you should be able to draw it with #x# in any quadrant. Definition of #sin(x)# #(#side opposite angle #x)//(#hypotenuse #)# Definition of #cos(90^@ -x)# #(#side adjacent to angle #(90^@-x))//(#hypotenuse #)# but #(#side opposite angle #x) = (#side adjacent to angle #(90^@-x)# Therefore #sin(x) = cos(90^@ -x)# Similarly #cos(x) = sin(90^@ - x)# These can also be proven using the sine and cosine angle subtraction formulas: #cos(alpha-beta)=cos(alpha)cos(beta)+sin(alpha)sin(beta)# #sin(alpha-beta)=sin(alpha)cos(beta)-cos(alpha)sin(beta)# Applying the former equation to #cos(90^@-x)#, we see that #cos(90^@-x)=cos(90^@)cos(x)+sin(90^@)sin(x)# #cos(90^@-x)=0*cos(x)+1*sin(x)# #cos(90^@-x)=sin(x)# Applying the latter to #sin(90^@-x)#, we can also prove that #sin(90^@-x)=sin(90^@)cos(x)-cos(90^@)sin(x)# #sin(90^@-x)=1*cos(x)-0*sin(x)# #sin(90^@-x)=cos(x)#

How to find the values? To learn the table, we should first know how We know that • tan θ = sin θ/cosθ • sec θ = 1/cos θ • cosec θ = 1/sin θ • cot θ = 1/cot θ Now let us discuss different values For sin For memorising sin 0°, sin 30°, sin 45°, sin 60° and sin 90° We should learn it like • sin 0° = 0 • sin 30° = 1/2 • sin 45° = 1/√2 • sin 60° = √3/2 • sin 90° = 1 So, our pattern will be like 0, 1/2, 1/√2, √3/2, 1 For cos For memorising cos 0°, cos 30°, cos 45°, cos 60° and cos 90° Cos is the opposite of sin. We should learn it like • cos 0° = sin 90° = 1 • cos 30° = sin 60° = √3/2 • cos 45° = sin 45° = 1/√2 • cos 60° = sin 30° = 1/2 • cos 90° = sin 0° = 0 So, for cos, it will be like 1, √3/2, 1/√2, 1/2, 0 -ad- For tan We know that tan θ = sin θ /cos θ So, it will be • tan 0° = sin 0° / cos 0° = 0/1 = 0 • tan 30° = sin 30° / cos 30° = (1/2)/ (√3/2) = 1/√3 • tan 45° = sin 45° / cos 45° = (1/√2)/ (1/√2) = 1 • tan 60° = sin 60° / cos 60° = (√3/2) / (1/2) = √3 • tan 90° = sin 90° / cos 90° = 1/0 = Not Defined = ∞ So, for tan, it is 0, 1/√3, 1, √3, ∞ -ad- For cosec We know that cosec θ = 1/sin θ For sin, we know 0, 1/2, 1/√2, √3/2, 1 So, for cosec it will be • cosec 0° = 1 / sin 0° = 1/0 = Not Defined = ∞ • cosec 30° = 1 / sin 40° = 1/(1/2) = 2 • cosec 45° = 1 / sin 45° = 1/(1/√2) = √2 • cosec 60° = 1 / sin 60° = 1/(√3/2) = 2/√3 • cosec 90° = 1 / sin 90° = 1/1 = 1 So, for cosec, it is ∞, 2, √2, 2/√3, 1 -ad- For sec We know that sec θ = 1/cos θ For cos, we know 1, √3/2, 1/√2, 1/2,...

How to find the values? To learn the table, we should first know how We know that • tan θ = sin θ/cosθ • sec θ = 1/cos θ • cosec θ = 1/sin θ • cot θ = 1/cot θ Now let us discuss different values For sin For memorising sin 0°, sin 30°, sin 45°, sin 60° and sin 90° We should learn it like • sin 0° = 0 • sin 30° = 1/2 • sin 45° = 1/√2 • sin 60° = √3/2 • sin 90° = 1 So, our pattern will be like 0, 1/2, 1/√2, √3/2, 1 For cos For memorising cos 0°, cos 30°, cos 45°, cos 60° and cos 90° Cos is the opposite of sin. We should learn it like • cos 0° = sin 90° = 1 • cos 30° = sin 60° = √3/2 • cos 45° = sin 45° = 1/√2 • cos 60° = sin 30° = 1/2 • cos 90° = sin 0° = 0 So, for cos, it will be like 1, √3/2, 1/√2, 1/2, 0 -ad- For tan We know that tan θ = sin θ /cos θ So, it will be • tan 0° = sin 0° / cos 0° = 0/1 = 0 • tan 30° = sin 30° / cos 30° = (1/2)/ (√3/2) = 1/√3 • tan 45° = sin 45° / cos 45° = (1/√2)/ (1/√2) = 1 • tan 60° = sin 60° / cos 60° = (√3/2) / (1/2) = √3 • tan 90° = sin 90° / cos 90° = 1/0 = Not Defined = ∞ So, for tan, it is 0, 1/√3, 1, √3, ∞ -ad- For cosec We know that cosec θ = 1/sin θ For sin, we know 0, 1/2, 1/√2, √3/2, 1 So, for cosec it will be • cosec 0° = 1 / sin 0° = 1/0 = Not Defined = ∞ • cosec 30° = 1 / sin 40° = 1/(1/2) = 2 • cosec 45° = 1 / sin 45° = 1/(1/√2) = √2 • cosec 60° = 1 / sin 60° = 1/(√3/2) = 2/√3 • cosec 90° = 1 / sin 90° = 1/1 = 1 So, for cosec, it is ∞, 2, √2, 2/√3, 1 -ad- For sec We know that sec θ = 1/cos θ For cos, we know 1, √3/2, 1/√2, 1/2,...

Note that the image below is only for #x# in Q1 (the first quadrant). If you wish you should be able to draw it with #x# in any quadrant. Definition of #sin(x)# #(#side opposite angle #x)//(#hypotenuse #)# Definition of #cos(90^@ -x)# #(#side adjacent to angle #(90^@-x))//(#hypotenuse #)# but #(#side opposite angle #x) = (#side adjacent to angle #(90^@-x)# Therefore #sin(x) = cos(90^@ -x)# Similarly #cos(x) = sin(90^@ - x)# These can also be proven using the sine and cosine angle subtraction formulas: #cos(alpha-beta)=cos(alpha)cos(beta)+sin(alpha)sin(beta)# #sin(alpha-beta)=sin(alpha)cos(beta)-cos(alpha)sin(beta)# Applying the former equation to #cos(90^@-x)#, we see that #cos(90^@-x)=cos(90^@)cos(x)+sin(90^@)sin(x)# #cos(90^@-x)=0*cos(x)+1*sin(x)# #cos(90^@-x)=sin(x)# Applying the latter to #sin(90^@-x)#, we can also prove that #sin(90^@-x)=sin(90^@)cos(x)-cos(90^@)sin(x)# #sin(90^@-x)=1*cos(x)-0*sin(x)# #sin(90^@-x)=cos(x)#

What is the Value of Cos 90 Degrees: The sine function, cosine function, and tangent function are the three most well-known trigonometric ratios in trigonometric functions. It is commonly specified for angles smaller than a right angle. Trigonometric functions are written as the ratio of two sides of a right triangle containing the angle, the values of which may be found in the length of various line segments around a unit circle. Degrees are often represented as 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360°. The first quadrant is considered to be located between 0 degreesand 90degrees. The third quadrant has angles between 180 degreesand 270 degrees, whereas the second quadrant contains angles ranging between 90 degreesand 180 degrees. The fourth quadrant covers the range of 270 degreesto 360 degrees. In the fourth quadrant, Cos stays positive. It is important to note that everything in the first one is positive. Tan is also positive in the second and third quadrant. For example, the distance from a point to the origin stays positive, but the X and Y coordinates might be either negative or positive. Thus, in the first quadrant, all coordinates are positive, but in the second quadrant, only sine and cosecant are positive. Tangent and cotangent are only positive in the third quadrant, but cosine and secant stay positive in the fourth. Let us now look at the value for cos 90 degrees, which is equal to zero, and how the values are calculated using the quadrants of a unit circl...

Cos 90 Degrees The value of cos 90 degrees is 0. Cos 90 degrees in radians is written as cos (90°×π/180°), i.e., cos (π/2) or cos (1.570796. . .). In this article, we will discuss the methods to find the value of cos 90 degrees with examples. • Cos 90°: 0 • Cos (-90 degrees): 0 • Cos 90° in radians: cos (π/2) or cos (1.5707963 . . .) What is the Value of Cos 90 Degrees? The value of cos 90 degrees is 0. Cos 90 degrees can also be expressed using the equivalent of the given We know, using ⇒ 90 degrees = 90°× (π/180°) rad = π/2 or 1.5707 . . . ∴ cos 90° = cos(1.5707) = 0 Explanation: For cos 90 degrees, the angle 90° lies on the positive y-axis. Thus cos 90° value = 0 Since the cosine function is a ⇒ cos 90° = cos 450° = cos 810°, and so on. Note: Since, cosine is an Methods to Find Value of Cos 90 Degrees The value of cos 90° is given as 0. We can find the value of cos 90 • Using Trigonometric Functions • Using Unit Circle Cos 90° in Terms of Trigonometric Functions Using • ±√(1-sin²(90°)) • ± 1/√(1 + tan²(90°)) • ± cot 90°/√(1 + cot²(90°)) • ±√(cosec²(90°) - 1)/cosec 90° • 1/sec 90° Note: Since 90° lies on the positive y-axis, the final value of cos 90° will be 0. We can use trigonometric identities to represent cos 90° as, • -cos(180° - 90°) = -cos 90° • -cos(180° + 90°) = -cos 270° • sin(90° + 90°) = sin 180° • sin(90° - 90°) = sin 0° Cos 90 Degrees Using Unit Circle To find the value of cos 90 degrees using the unit circle: • Rotate ‘r’ anticlockwise to form 90° angle w...